Mrs. English Fox Creek Jr. High BCESD. What is an equation? How are equations useful in solving real- world problems? How do you solve an algebraic

I CAN USE VARIABLES TO SET UP AND SOLVE

REAL-WORLD PROBLEMS USING EQUATIONS

Mrs. English Fox Creek Jr. High BCESD

ESSENTIAL QUESTIONS What is an equation? How are equations useful in solving real-

world problems? How do you solve an algebraic

equation? What is a variable? How do you isolate

the variable to solve an equation?

ARITHMETIC VS ALGEBRA We can solve real-world problems using

both arithmetic and algebra. If we use the arithmetic method, we

would use only numbers. If we use the algebra method, we would

use numbers and variables (letters) Either way, we will end up with the

same answer.

EXAMPLE The sum of two different sides of the

rectangle is 17 inches. What is the perimeter of the rectangle?


rectangle is 17 inches. What is the perimeter of the rectangle? I know that perimeter means the distance

around something, so I need to find out how far it is around the whole rectangle




This side

and this side add up for a total of 17 inches




This side


To find the perimeter, I need to find the distance around the other half of the rectangle.




This side



17 x 2 = ? Or 1/2(x) = 17




This side



17 x 2 = ? Or 1/2(x) = 1717 x 2 = 34 x 2 x 2 x = 34

TRY THIS! The sum of two different sides of a

rectangle is 24 centimeters. What is the perimeter of the rectangle?

EXAMPLE A corn field is 500 feet wide. If you know

the perimeter is 1600 feet, what is the corn field’s length?

EXAMPLE A corn field is 500 feet wide. If you know

the perimeter is 1600 feet, what is the corn field’s length?

Using arithmetic Using algebra1600-500-500 = 600 1600-2(500)=2x600 / 2 = 300 1600-1000=2x

600 = 2x300 = x

TRY THIS! A soybean field is 420 feet wide. If you

know the field has a perimeter of 1600 feet, what is the field’s length?

EXAMPLE Your dog gave birth to 6 puppies. You

want to keep them all, but you were told you had to sell all but 1 of them. If you earned $325, how much did each puppy cost?


want to keep them all, but you were told you had to sell all but 1 of them. If you earned $325, how much did each puppy cost?How many puppies did you sell?


want to keep them all, but you were told you had to sell all but 1 of them. If you earned $325, how much did each puppy cost?How many puppies did you sell? 5



Using arithmeticUsing algebra$325 / 5 = 5x = $325



Using arithmeticUsing algebra$325 / 5 = $65 5x = $325

5 5x = $65

EXAMPLE Your dog gave birth to 6 puppies. You want

to keep them all, but you were told you had to sell all but 1 of them. If you earned $325, how much did each puppy cost?How many puppies did you sell? 5

Using arithmeticUsing algebra$325 / 5 = $65 5x = $325 OR (6-1)x = $325

5 5 5x = $325x = $65 x = $65

TRY THIS! Your dog gave birth to seven puppies.

Your mom told you to sell all but one. If you earned $480, how much did you sell each puppy for?

EXAMPLE Your dad just got his paycheck and

decides to pay for you and your three friends to go bowling. It costs $6.00 per person to get in. Bowling shoes cost $2.50 per person to rent. After bowling for awhile, your dad buys a soda for each person. How much does the soda cost if your dad spent a total of $42.00 at the bowling alley?


decides to pay for you and your three friends to go bowling. It costs $6.00 per person to get in. Bowling shoes cost $2.50 per person to rent. After bowling for awhile, your dad buys a soda for each person. How much does the soda cost if your dad spent a total of $42.00 at the bowling alley?How many people went bowling?


decides to pay for you and your three friends to go bowling. It costs $6.00 per person to get in. Bowling shoes cost $2.50 per person to rent. After bowling for awhile, your dad buys a soda for each person. How much does the soda cost if your dad spent a total of $42.00 at the bowling alley?How many people went bowling? 4


decides to pay for you and your three friends to go bowling. It costs $6.00 per person to get in. Bowling shoes cost $2.50 per person to rent. After bowling for awhile, your dad buys a soda for each person. How much does the soda cost if your dad spent a total of $42.00 at the bowling alley?How many people went bowling? 4We need to multiply everything by 4.

EXAMPLE

Arithmetic$42 – 4($6) – 4($2.50)= sodaThen divide the cost of soda by 4 bowlers

Algebra4($6) + 4($2.50) + 4(s) = $42.00

EXAMPLE

Arithmetic$42 – 4($6) – 4($2.50)= soda$42 – $24 – $10 = soda Then divide the cost of soda by 4 bowlers

Algebra4($6) + 4($2.50) + 4(s) = $42.00

EXAMPLE

Arithmetic$42 – 4($6) – 4($2.50)= soda$42 – $24 – $10 = soda $8= soda Then divide the cost of soda by 4 bowlers $8/4 = $2

Algebra4($6) + 4($2.50) + 4(s) = $42.00

EXAMPLE


Algebra4($6) + 4($2.50) + 4(s) = $42.00 $24 + $10 + 4s = $42.00

EXAMPLE


Algebra4($6) + 4($2.50) + 4(s) = $42.00 $24 + $10 + 4s = $42.00$34 + 4s = $42.00

EXAMPLE


Algebra4($6) + 4($2.50) + 4(s) = $42.00 $24 + $10 + 4s = $42.00$34 + 4s = $42.00 -$34 -$34

EXAMPLE


Algebra4($6) + 4($2.50) + 4(s) = $42.00 $24 + $10 + 4s = $42.00$34 + 4s = $42.00 -$34 -$34 4s = $8 s = $2

TRY THIS! Your mom just got her paycheck and

takes you and four friends to play mini golf. It costs $4.50 per person to play, and another $1.50 per person to rent a putter. After a round of mini golf, your mom also buys you each a personal pizza. If she spent $45 altogether, how much did each pizza cost?

EXAMPLE Harry is making spaghetti. He went to

the store and spent $38.00. He bought 4 cans of spaghetti sauce for $2.25 each, 2 boxes of whole wheat pasta for $3.00 each, a block of parmesan cheese for $6.00, and 4 pounds of ground beef. How much did each pound of ground beef cost?



4($2.25) + 2($3.00) + 1($6.00) + 4(b) = $38.00



4($2.25) + 2($3.00) + 1($6.00) + 4(b) = $38.00

$9 + $6 + $6 + 4b = $38.00



4($2.25) + 2($3.00) + 1($6.00) + 4(b) = $38.00

$9 + $6 + $6 + 4b = $38.00 $21 + 4b = $38.00



4($2.25) + 2($3.00) + 1($6.00) + 4(b) = $38.00

$9 + $6 + $6 + 4b = $38.00 $21 + 4b = $38.00 -$21 -$21



4($2.25) + 2($3.00) + 1($6.00) + 4(b) = $38.00

$9 + $6 + $6 + 4b = $38.00 $21 + 4b = $38.00 -$21 -$21 4b = $17

EXAMPLE Harry is making spaghetti. He went to the

store and spent $38.00. He bought 4 cans of spaghetti sauce for $2.25 each, 2 boxes of whole wheat pasta for $3.00 each, a block of parmesan cheese for $6.00, and 4 pounds of ground beef. How much did each pound of ground beef cost?

4($2.25) + 2($3.00) + 1($6.00) + 4(b) = $38.00

$9 + $6 + $6 + 4b = $38.00 $21 + 4b = $38.00 -$21 -$21 4b = $17 4b/4 = $17/4 b = $4.25

TRY THIS! Moe is making chicken tacos. He spent

$15.75 at the store. He purchased 3 tomatoes for $0.75 each, a bag of cheese for $2.50, 2 onions for $0.50 each, two packages of tortillas for $2.50 each, and 2 pounds of chicken. How much did each pound of chicken cost?

ESSENTIAL QUESTIONS What is an equation?

Equations are two values that are equal How are equations useful in solving real-

world problems?Equations can be translated from real-word

problems How do you solve an algebraic equation?

Equations can be solved by isolating the variable

What is a variable? How do you isolate the variable to solve an equation?A variable is a letter that represents an

unknown value. We isolate the variable by performing inverse operations.

Documents

Mrs. English Fox Creek Jr. High BCESD. What is an equation? How are equations useful in solving real- world problems? How do you solve an algebraic